Econ 344
Problem Set #3
Assigned:Tu. Oct. 7, 2008
Due:Th. Oct. 14, 2008
Corresponding Chapters:
Part I Multiple Choices (2*9=18 points)
1.When people behave in ways that involve increased risk because they have insurance, this is known as
a)adverse selection.
b)moral hazard.
c)asymmetric information.
d)a HMO.
b
2Health care markets may be inefficient because of
a)poor information.
b)adverse selection.
c)moral hazard.
d)all of the above.
e)none of the above.
d
3An actuarially fair return means
a)returns on investments are indexed to the stock market.
b)returns on investments have to be positive.
c)benefits received, on average, would be equal to the premiums paid.
d)premiums for insurance are generally paid by the government.
e)none of the above.
c
4When the average buyer of an insurance policy is likely to have higher risk than others in his class, this is known as
a)adverse selection.
b)moral hazard.
c)asymmetric information.
d)a HMO.
e)none of the above.
A
5.Asymmetric information generally implies
a)information between parties is not equal.
b)all parties are fully informed.
c)information is costless.
d)information is too costly to transmit.
e)a and c.
a
11. Removing "welfare lock" means which of the following?
a. Government should not incarcerate the fathers of children in single-mother welfare homes because it reduces child support payments.
b. Government should unlink cash welfare from other in-kind benefits.
c. Government should reduce the benefits reduction rate to increase the benefits of working.
d. All welfare payments should be given based on unchangeable characteristics.
e. None of the above is correct.
Answer: B (Pages 504-506)
- Which of the following is NOT one of the three forms or moral hazard related to health insurance (HI)?
- With HI, people are less likely to try their best to live a healthy life style.
- People tend to over-consume health care services if they have HI.
- Those who think they have a higher risk of getting cancer are more likely to buy HI.
- If people know that they will have access to health care even if they do not have HI, they will not buy HI.
c---is adverse selection
. 8. The Earned Income Tax Credit (EITC)
a)provides more income to those people on welfare.
b)is a tax on low income workers.
c)provides additional tax credits to low income workers.
d)is a tax break for the wealthiest Americans.
e)was eliminated by the Bush administration.
c
9.Which is the largest cash transfer program for the poor?
a)TANF
b)Medicare
c)SSI
d)Medicaid
e)Section 8
a
2. Medicaid is administered by the ______and is financed by ______.
a. states; general revenues
b. states; a payroll tax levied on employees and employers
c. federal government; general revenues
d. federal government; a payroll tax levied on employers
e. federal government; a payroll tax levied on employees
Answer: A (Page 445)
True/False/Uncertain----explain (2*3=6pts.)
10.Under federal tax law, employerprovided health insurance is not subject to taxation.
T
12.One reason for the recent increases in health care costs is the aging of the American population.
T
III. Open questions
- (20 points) Purpose—understand how cost sharing may alleviate moral hazard problem.
Anna’s demand each year for visit to doctors is given by: Q = 10 - .05P, where Q is the number of visits, and P is the price Anna pays for a visit.
- (5 points) How many visits would Anna take if P=$80 and she is not insured?
Q=10-.05*80=6.
- (7 points) How many visits would Anna take if P=$80 but she is insured with a co-insurance payment of 25%? Suppose P=$80 is also the true social cost of visits to doctors, what is the social welfare loss from this co-insurance program for Anna?
The price Anna pays is: .25*80=20
Q=10-.05*20=9.
Welfare loss=.5*(9-6)*(80-20)=90
- (7 points) Please draw Anna’s demand curve and show the visits she takes and the price she pays in part a. and b. Please also indicate the welfare loss in b.
d (6 points) Will a co-pay of $20 per visit improve social welfare relative to the co-insurance policy in part b.? Why and by how much, if any?
A co-pay (or co-payment) is a fixed dollar amount the patient must pay per unit of health care provided. In this question, a co-pay of $20 per visit happens to equal the co-insurance payment of 25% (80*25%=20). Thus, here a co-pay of $20 per visit will not improve social welfare relative to the co-insurance policy in part b.
2. Expected utility of insurance (20 pts)
Johnny is considering whether to buy health insurance His utility is given by U(I)= √I where I is his yearly income equal to $25,000. However there is a 5% chance that he’ll fall sick with a avian flu virus which will cost him $5000.
- what is his expected utility of not buying any insurance?
EU = .05* √(25000-5000) + .95 √(250000) = 157.28
b. what is the actuarially fair premium for the health insurance in this case?
.05(5000) + .95(0) =250
c. Assuming that the premium is actuarially fair, what is th expected utility associated with buying full insurance (ie insuring all $5,000 of potential loss)? What is the expected utility associated with insuring only half of the loss ($2500)? Is Johnny going to choose full insurance or partial insurance?
Full Ins .05 *√(20000-250+5000) +.95 √(25000-250) =157.32
Partial .05 * √(20000-125 +2500) + .95 (25000-125) = 157.31
Full insurance is preferred.
3. Jackie spends her money on food and all other goods. Right now, she has an income
of $600 per month. Compare two alternative welfare programs in which she could participate:
program A would provide her with a monthly check of $300 and program B
would provide her with $400 a month in credits that can be spent only on food.
a. Draw Jackie’s budget constraints in each of these two cases.
The solid line in the figure shows Jackie’s budget constraint with a $300 cash grant
(program A). The grant, combined with her $600 income, allows her to buy $900 worth of
food and other goods in any combination that totals $900. The dashed line shows Jackie’s
budget constraint with a $400 food subsidy (program B). Jackie has only $600 to spend
on all other goods, but if she chooses to spend it all on food, she could buy $1,000 worth
of food. More likely, Jackie will choose some combination along this line.
b. Draw representative indifference curves that would reflect each of these three scenarios
(see the graph in a).
(i) Jackie prefers program A to program B.
The indifference curve labeled (i) is consistent with preferences that favor the cash
grant over the subsidy.
CHAPTER 17 / Income Distribution and Welfare Programs - 7 -
(ii) Jackie prefers program B to program A.
The curve labeled (ii) is consistent with preferences that favor the larger in-kind subsidy.
The (ii) preferences are heavily weighted toward food: this person wishes to spend
the lion’s share of her budget on food, so a food subsidy of $400 is worth more to her
than $300 in cash.
(iii) Jackie is indifferent between the two programs.
The indifference curve labeled (iii) indicates someone who is exactly indifferent between
a $300 cash grant and a $400 in-kind subsidy. With the $300 check program, the
individual with these preferences works more and gets to consume about $700 worth of
“other goods” and less than $400 in food. The $400 food-only program induces the
worker to consume only $600 of other goods and $400 in food. There is a trade-off between
these two options: the latter option involves more total consumption, but the former
option has a more desirable balance between the two types of good. The indifference
curve indicates that the worker is indifferent to this tradeoff.
4. An individual can earn $12 per hour if he or she works. Draw the budget constraints
that show the monthly consumption–leisure trade-off under the following three welfare
programs.
In each graph, assume that a person can work at most 24 hours per day times 30 days
per month for a total of 720 hours. Thus, the axis intercepts, in the absence of any program,
are 720 × $12 = $8,640 in consumption and 720 hours of leisure.
a. The government guarantees $600 per month in income and reduces the benefit by
$1 for each $1 of labor income.
The equivalent of $600 of income is 50 hours of labor (at the $12 wage) or 720 – 50
= 670 hours of leisure.
b. The government guarantees $300 per month in income and reduces that benefit by
$1 for every $3 of labor income.
The equivalent of $300 of income is 25 hours of labor or 695 hours of leisure. The entire
$300 guarantee would be eliminated after the recipient earned $900 or worked 900/12
= 75 hours, which yields 720 – 75 = 645 hours of leisure.
c. The government guarantees $900 per month in income and reduces that benefit by
$1 for every $2 in labor income, until the benefit reaches $300 per month. After that
point, the government does not reduce the benefit at all.
This program yields a wage rate of $6 per hour up to 100 hours of work per month.
The reduction ends after $600 is deducted, which occurs at 100 hours per month (100 × 6
CHAPTER 17 / Income Distribution and Welfare Programs - 3 -
Leisure (hours)
$8,640
$600
0 670 720
Consumption
$8,640
$900
$300
0 645 695 720
Consumption
Leisure (hours)
= $600). Wages are 100 × $12 = $1,200, plus benefits of $300, for total consumption of
$1,500 and 720 – 100 = 620 hours of leisure. At greater than 100 hours, the new budget
line parallels the baseline $12 per hour line but is $300 higher. As a result, the new yintercept
is $8,640 + $300 = $8,940.
(need to scan in diagrams for here)
5. Suppose the government decided to subsidize health insurance for the currently uninsured,
requiring participants to pay half of their health insurance costs up to 10% of
total family income.
a. How might this policy affect the use of medical care by the uninsured and their
health?
This policy might reduce the number of uninsured people in the population by making
CHAPTER 16 / Health Insurance II: Medicare, Medicaid, and Health Care Reform - 2 -
insurance more affordable. If the previously uninsured population were able to obtain insurance
affordably, those who don’t have insurance because they cannot afford it would
obtain it. The 10% cap would reduce the problem of high premiums for individuals who
purchase insurance separately from large employers or other risk-pooling entities, but it
would not completely eliminate that problem. It is likely that if the previously uninsured
bought insurance privately, it would be for a high premium because of the lack of risk
pooling. Once insured, this population would face lower costs for medical care and so
would be more likely to seek it. Although there seems to be little evidence that more generous
benefits improve health outcomes relative to less generous benefits, the absence of
any insurance at all is associated with worse health outcomes. Thus, to the extent people
avail themselves of this opportunity, their health is likely to improve.
b. How might this policy affect the employer provision of health insurance?
This policy might dissuade employers from offering health insurance to employees
because they would know that alternative coverage is available from the government.
Large employers have a cost advantage in providing health insurance to their employees:
they offer insurance companies large pools of enrollees who have not adversely selected
coverage, they reduce administrative costs by covering many enrollees with a single contract,
and because premiums are paid with pretax dollars, it is cheaper for employers to
offer insurance than to increase wages by an equivalent dollar amount. If this policy
crowded out employer provision, some of these sources of efficiency would be lost.
c. How might this policy affect hours of labor supplied by workers?
There are two ways this might discourage work. First, employer-provided health insurance
is typically linked to full-time work requirements. This may provide a strong incentive
for workers to take full-time jobs instead of part-time jobs. If workers can instead
get government-subsidized health insurance while working only part-time, they may
switch to part-time work.
Second, consider a worker whose family income is below 20%of the cost of medical care. Then paying half of the cost of health insurance would leadthem to spend more than 10% of their income on health insurance and, since the government
limits the amount families pay to a maximum of 10% of family income, the government
would have to contribute the difference. If the worker were to choose to work more,
his family income would rise, so 10% of his income would be higher, and the government
would contribute less for health insurance. Effectively, the 10% income limit forces lowincomeworkers to spend some of their additional earnings on insurance that the governmentwould have provided if they didn’t work. This is like a tax on working, which
discourages work.